Chapter 3

Recursive Thinking

The branches of a blue spruce tree (Figure 3.1) follow an interesting pattern. The trunk of the tree is a large central stem, with branches coming off each side. These branches also have thinner stems coming off them, and so on, until you reach the level of the needles. A branch looks like a smaller copy of the whole tree, and even a small twig looks like a miniature branch. This is a picture of recursion.

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Figure 3.1 A recursive blue spruce.

The natural phenomenon of recursion pervades many areas of mathematics. In this chapter, you will learn how to work with recursive structures. You will develop the ability to ...

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